Question

How do you find the slope given `y + 4x = 5`?

Answer 1

standard form is `" "y=-4*x+5`.
-4 is the slope & 5 the y-intercept.

Explanation:

standard form is `y=mx+c, :. y=-4*x+5`
-4 is the slope & 5 the y-intercept.

Answer 2

slope =`color(white)(.) - 4`

Explanation:

The standardised equation for a straight line graph is:

`" "y=mx+c`

As `x` can be assigned any value you chose it is called the independent variable

As the value of `y` depends on the value you assign to `x` it is called the dependant variable

The slope (proper name is gradient ) is `m` this represents the amount of up or down for the amount along as you read left to right.
If m is negative then it is a downward slop. If m is positive then it is an upwards slop.

The constant `c` just lifts or lowers the graph. If it is `-c` then the line is lowered by that amount. If it is `+c` then the graph is raised by that amount.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given: `color(brown)(y+4m=5)`

Converting this equation to standard form

Subtract `color(blue)(4m)` from both sides giving:

`" "color(brown)(y+4mcolor(blue)(-4m)" "=" "5color(blue)(-4m))`

`y+0=-4m+5`

`" "color(green)(y=-4x+5)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(magenta)(" So the slope is "-4)`.

This means for 1 along the x-axis y goes down by 4